This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A088688 #14 Aug 29 2025 07:17:31
%S A088688 0,1,3,6,12,27,63,141,297,594,1146,2169,4095,7827,15291,30582,62256,
%T A088688 127791,262143,534129,1078101,2156202,4282878,8477181,16777215,
%U A088688 33288711,66311703,132623406,266043972,534479427,1073741823,2154658101
%N A088688 Binomial transform of A088689.
%H A088688 Harvey P. Dale, <a href="/A088688/b088688.txt">Table of n, a(n) for n = 0..1000</a>
%H A088688 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6).
%F A088688 a(n) = 2^n - cos(Pi*n/3) - 3^(n/2)*sin(Pi*n/6)/sqrt(3).
%F A088688 O.g.f.: -x(1-3x+3x^2+x^3)/[(2x-1)(x^2-x+1)(3x^2-3x+1)]. - _R. J. Mathar_, Apr 02 2008
%t A088688 Table[Sum[Binomial[n,k] * Mod[k*Floor[3*(k+1)/2] - 2*k, 3], {k, 0, n}], {n, 0, 40}] (* _Vaclav Kotesovec_, Oct 30 2017 *)
%t A088688 CoefficientList[Series[-x(1-3x+3x^2+x^3)/((2x-1)(x^2-x+1)(3x^2-3x+1)),{x,0,40}],x] (* or *) LinearRecurrence[{6,-15,20,-15,6},{0,1,3,6,12},40] (* _Harvey P. Dale_, Aug 28 2025 *)
%Y A088688 Cf. A001045.
%K A088688 easy,nonn,changed
%O A088688 0,3
%A A088688 _Paul Barry_, Oct 06 2003